1. Field of the Invention
The present invention relates to an apparatus for providing equalization in orthogonal multi-carrier data transmission systems, and more particularly relates to an apparatus for providing per-bin decision feedback equalization (DFE) for advanced OQAM-based multi-carrier wireless data transmission systems, as an example of a class of multi-carrier systems with spectrally shaped and over-lapped sub-channels.
2. Description of Related Art
Multi-carrier (MC) data transmission systems were traditionally applied as an alternative to conventional single-carrier (SC) systems in situations where the latter would inevitably require adaptive equalization. Toward this end, in the early MC data transmission systems of the Kineplex type (see for example, R. R. Mosier and R. G. Clabauch, “Kineplex, a bandwidth-efficient binary transmission system,” Trans. AIEE (Comm. and electronics), pp. 723-728, January 1958), and its FFT-based implementation (see for example S. B. Weinstein and P. M. Ebert, “Data transmission by frequency multiplexing using the DFT,” IEEE Trans. Com. Techn. Vol. COM-19, pp. 528-634, October, 1971), as well as in the newer applications of partially shaped rectangular sub-channel signaling elements in the broadcasting (see for example, B. LeFloch R. Halbert-Lassalle and D. Castelain, “Digital sound broadcasting to mobile receivers,” IEEE Trans. Cons. Electr., Vol. 35, No. 3, pp. 493-503, August 1989), wireless LAN (see for example, D. Dardari and V. Tralli, “Performance and design criteria for high-speed indoor services,” Proc. IEEE Globecom'97, Phoenix, Ariz., pp. 1306-1311, November 1997), and the currently considered 4G cellular system proposals, a time-guard interval, so called cyclic prefix (CP), is used, with the length chosen to be longer than the expected length of channel impulse response.
Since the utilization of CP reduces spectral efficiency, the use of relatively high number of sub-channels is preferred. This in turn leads to an increased peak-to-average power ratio and a wide range of associated problems regarding power-efficient amplification. These problems include: requiring a relatively large dynamic range for analog-to-digital (ADC) conversion; an increased system delay and memory requirements; and a more pronounced impact of multiplicative distortions (carrier offset, phase jitter and time-selective fading) in wireless applications. The sole reliance on the guard-time interval in OFDM wireless applications proves insufficient in case of multi-path delay spreads exceeding the length of CP, and, much more importantly, the constrained sub-channel bandwidths preclude any utilization of implicit multi-path diversity. Contrary to the often claimed feature of C(coded)OFDM (see for example, B. LeFloch R. Halbert-Lassalle and D. Castelain, “Digital sound broadcasting to mobile receivers,” IEEE Trans. Cons. Electr., Vol. 35, No. 3, pp. 493-503, August 1989), to exploit the implicit frequency of multi-path channels, the underlying utilization of coding with interleaving merely counteracts the appearance of bursty errors at the expense of a large data transmission overhead.
On the other hand, the orthoganally frequency-division multiplexed (OFDM) multi-carrier data transmission system with Nyquist-type shaped sub-channel spectra and the staggered (S-), or offset (O-) quadrature amplitude modulation (QAM) in its sub-channels, proposed in B. R. Salzberg, “Performance of efficient parallel data transmission system,” IEEE Trans. Comm. Technology, Vol. COM-15, pp. 805-811, December 1967, based on the previously established orthogonality conditions (see for example R. W. Chang, “Synthesis of band-limited orthogonal signals for multi-carrier data transmission,” The Bell Syst. Techn. Journal, Vol. 45, pp. 1775-1796, December 1996), is maximally efficient spectrally. It was first shown in B. Hirosaki, “An analysis of automatic equalizer for orthogonally multiplexed QAM systems,” IEEE Trans. on Comm., Vol. 28, No. 1, pp. 73-83, January 1980, that the adaptive equalization in OQAM-based MC system can be carried out by using per-subchannel equalizers. This “dual” equalization cancels both the inter- and intra sub-channel interference (ISI and ICI), and basically does not impose any constraint regarding preferable number of sub-channels, leaving such a choice to be based on other system implementation and transmission impairment related issues. However, because the equalization method of Hirosaki involves the re-alignment of QAM in-phase and quadrature components and consequently exhibits a strong interaction between linear distortion and carrier/sampling phase offset compensation, it is difficult to implement (see for example, B. Hirosaki, “Generalized differential coding theorem and its application,” Electronics and Communications in Japan, Vol. 67-B, No. 12, pp. 46-53, 1984).
An alternative equalization method, partly introduced in S. Nedic, “An unified approach to equalization and echo-cancellation in multi-carrier OQAM-based data transmission,” Globecom'97, Phoenix, Ariz., 1997, relies on the notion of the inherent half QAM symbol signaling intervals and as result, is more general, easier to implement, and readily extendable to other orthogonal multi-carrier data transmission systems, such as time-limited orthogonal (TLO)(see for example, R. Li and G. Stette, “Time-limited orthogonal multi-carrier modulation schemes,” IEEE Trans. on Comm., Vol. 43, No. 2/3/4, pp. 1269-1272, February/March/April, 1995 and J. Alhava, M. Renfors, “Adaptive sine-modulated/cosine-modulated filter bank equalizer for transmultiplexers,” ECCTD'01, August 28-31, Espoo, Finland, 2001), discrete wavelet multi-tone (DWMT)(see for example, W. Yang, and T-Sh. P. Yum, “A multirate wireless system using wavelet packet modulation,” VTC'97). The commonalities between seemingly different OQAM-MC and DWMT signaling formats, and thus the general applicability of per-bin linear and DFE equalization methods, can be established by simple frequency shift in respective defining equations, as discussed below.
Starting from its defining relation, the OQAM-MC transmit signal can be expressed in concise form by the following expression, pertaining to the conventional modulation conception:
                                          s            ⁡                          (              t              )                                =                                    ℜ              e                        ⁢                          {                                                                                          ∑                                                                                                                                                          k                        =                        0                                            ⁢                                                                                                                                                          N                        -                        1                                            ⁢                                                                                                                            ⁡                                      [                                                                  ∑                                                  m                          =                                                      -                            ∞                                                                                                    +                          ∞                                                                    ⁢                                                                                          ⁢                                                                        α                                                      k                            ,                            m                                                                          ·                                                  g                          ⁡                                                      (                                                          t                              -                                                              m                                ⁢                                                                  T                                  2                                                                                                                      )                                                                                                                ]                                                  ·                                                      exp                    ⁡                                          [                                              j                        ⁡                                                  (                                                      2                            ⁢                                                          π                              ·                                                              f                                k                                                                                      ⁢                            t                                                    )                                                                    ]                                                        .                                            }                                      ,        with                            (        A        )            αk,m=ak,m·exp {j[(−1)k+(−1)m][(−1)(k−1)(m−1)](Π/4)}  (B)
Above, the parameter T is the QAM symbol interval duration and fk is the k-th sub-channel central frequency, nominally defined by k/T. Variables ak,m in equation (B), for two consecutive even and odd values of m, represent the real and imaginary parts of complex QAM data symbols in the k-th sub-channel. It can be easily seen that (B) corresponds to following, commonly used definition:
      α          k      ,      m        =      {                                                      a                              k                ,                m                                      ,                                                            ⁢                                          for                ⁢                                                                  ⁢                even                ⁢                                                                  ⁢                m                ⁢                                                                  ⁢                and                ⁢                                                                  ⁢                odd                ⁢                                                                  ⁢                k                            ;                                                                                      -                              ja                                  k                  ,                  m                                                      ,                                                            ⁢                                          for                ⁢                                                                  ⁢                odd                ⁢                                                                  ⁢                m                ⁢                                                                  ⁢                and                ⁢                                                                  ⁢                odd                ⁢                                                                  ⁢                k                            ;                                                                                      -                              ja                                  k                  ,                  m                                                      ,                                                            ⁢                                          for                ⁢                                                                  ⁢                even                ⁢                                                                  ⁢                m                ⁢                                                                  ⁢                and                ⁢                                                                  ⁢                even                ⁢                                                                  ⁢                k                            ;                                                                                      a                              k                ,                m                                      ,                                                            ⁢                          for              ⁢                                                          ⁢              odd              ⁢                                                          ⁢              m              ⁢                                                          ⁢              and              ⁢                                                          ⁢              even              ⁢                                                          ⁢                              k                .                                                        
On the other side, the DWMT transmit signal is commonly described in its pass-band signaling form as
            s      ⁢              (        t        )              =                  ℜ        e            ⁢              {                                            ∑                                                                                                  k                =                0                            ⁢                                                                                                  N                -                1                            ⁢                                                                            ⁢                                    ∑                              m                =                                  -                  ∞                                                            +                ∞                                      ⁢                                                  ⁢                                                            α                                      k                    ,                    m                                                  ·                                  g                  ⁢                                      (                                          t                      -                                              m                        ⁢                                                  T                          2                                                                                      )                                                              ⁢                              exp                ⁡                                  [                                                            j2π                      ·                                                                        f                          k                          ′                                                ⁢                                                  (                                                      t                            -                                                          m                              ⁢                                                              T                                2                                                                                                              )                                                                                      +                                          θ                      k                                                        ]                                                                    }              ,with θk=(−1)k(π/4) and f′k=(2k+1)(½T). 
Transformed to the form of a sum of conventionally modulated base-band data signals, the DWMT signal takes the form
            s      ⁡              (        t        )              =                  ℜ        e            ⁢              {                                                            ∑                                                                                                                k                  =                  0                                ⁢                                                                                                                N                  -                  1                                ⁢                                                                                        ⁡                          [                                                ∑                                      m                    =                                          -                      ∞                                                                            +                    ∞                                                  ⁢                                                                  ⁢                                                      α                                          k                      ,                      m                                        ′                                    ·                                      g                    ⁡                                          (                                              t                        -                                                  m                          ⁢                                                      T                            2                                                                                              )                                                                                  ]                                ·                                    exp              ⁡                              [                                  j                  ⁡                                      (                                          2                      ⁢                                              π                        ·                                                  f                          k                          ′                                                                    ⁢                      t                                        )                                                  ]                                      .                          }              ,  whereα′k,m=ak,m·exp {j[(−1)k(π/4)−(π/2)m(2k+1)]}.
After shifting the above signal in frequency for −½T, by multiplying bracketed term with exp [−j(2Π/2T+Π/4)], it takes the form
            s      ⁡              (        t        )              =                  ℜ        e            ⁢              {                                            ∑                                                                                                  k                =                0                            ⁢                                                                                                  N                -                1                            ⁢                                                                            ⁢                                    ∑                              m                =                                  -                  ∞                                                            +                ∞                                      ⁢                                                  ⁢                                                            α                  ~                                                  k                  ,                  m                                ′                            ·                              g                ⁡                                  (                                      t                    -                                          m                      ⁢                                              T                        2                                                                              )                                            ·                                                exp                  ⁡                                      [                                          j                      ⁡                                              (                                                  2                          ⁢                                                      π                            ·                                                          f                              k                                                                                ⁢                          t                                                )                                                              ]                                                  .                                                    }              ,  with{tilde over (α)}′k,m=ak,m·exp {j[(1+(−1)k)(π/4)−(π/2)m(2k+1)]}.
can be easily verified that the data symbols above can be represented in following way, as
            α      ~              k      ,      m        ′    =      {                                                                      a                                  k                  ,                  m                                            ·              Y                        ,                                                            ⁢                                          for                ⁢                                                                  ⁢                even                ⁢                                                                  ⁢                m                ⁢                                                                  ⁢                and                ⁢                                                                  ⁢                odd                ⁢                                                                  ⁢                k                            ;                                                                                                      -                                  ja                                      k                    ,                    m                                                              ·              Y                        ,                                                            ⁢                                          for                ⁢                                                                  ⁢                odd                ⁢                                                                  ⁢                m                ⁢                                                                  ⁢                and                ⁢                                                                  ⁢                odd                ⁢                                                                  ⁢                k                            ;                                                                                                      -                                  ja                                      k                    ,                    m                                                              ·              Y                        ,                                                            ⁢                                          for                ⁢                                                                  ⁢                even                ⁢                                                                  ⁢                m                ⁢                                                                  ⁢                and                ⁢                                                                  ⁢                even                ⁢                                                                  ⁢                k                            ;                                                                                                      a                                  k                  ,                  m                                            ·              Y                        ,                                                            ⁢                                          for                ⁢                                                                  ⁢                odd                ⁢                                                                  ⁢                m                ⁢                                                                  ⁢                and                ⁢                                                                  ⁢                even                ⁢                                                                  ⁢                k                            ,                                          where γ alternates between +1 to −1 for every second pair of signaling intervals T/2.
Since changing sign of data symbols bears no relevance to system orthogonality, by comparing with originating expressions, (equation 1 in the main part of application), basic commonality among the OQAM-MC and DWMT signaling formats can be established. That means that whatever impulse response g(t), or window w(t), may satisfy the orthogonality criteria for one system, it will apply to the other system, and vice versa. This fully applies to the TLO-MC signaling format as well.
The per-bin equalization for multi-carrier signals with overlapped and well confined sub-channel spectra resembles the application of conventional equalization to single-carrier (SC) systems or to sub-channels in filtered multi-tone (FMT) format with non-overlapped sub-channel spectra (see for example, R. Vallet and K. H. Taieb, “Fraction spaced multi-carrier modulation,” Wireless Personal Communications 2: 97-103, 1995, Kulwer Academic Publishers). However, the overlapping of sub-channel spectra influences both the spectral (transfer function) and convergence properties of intrinsically base-band type per-bin equalizers and involves decisions from adjacent bins in the non-linear, decision feed-back (DFE) variant of interest here. One should bear in mind that it is the application of sub-channels bandwidths exceeding the multi-path fading coherence band-width where application of DFE equalization can effectuate substantial multi-path diversity gain, in line with the early established results regarding implicit diversity feature (see for example, P. Monsen, “Digital transmission performance on fading dispersive diversity channels,” IEEE Trans. On Comm., Vol. COM-21, No. 1, pp. 33-39, January, 1972). Wider sub-channels are also favorable for better suppression of narrow-band interference (NBI) impairments.